Question

What is the answer to this???

Answer 1

Answer:

Option C.

Step-by-step explanation:

It is given that each pair of polygon is similar.

From the given figure it is clear that,

$\angle E=\angle B=83^\circ$

$\angle F=\angle C=69^\circ$

$\angle G=\angle D=129^\circ$

$\angle H=\angle A=79^\circ$

Corresponding angles of similar figures are congruent. So,

$EFGH\sim BCDA$

Corresponding sides of similar figures are proportional.

$\dfrac{GH}{DA}=\dfrac{HE}{AB}$

$\dfrac{6.4}{3.2}=\dfrac{9.6}{4x}$

$2=\dfrac{9.6}{4x}$

$8x=9.6$

$x=1.2$

The value of x is 1.2 units.

$AB=4x=4(1.2)=4.8$

$CB=6x-2=6(1.2)-2=7.2-2=5.2$

Scale factor is

$k=\dfrac{EF}{BC}=\dfrac{10.4}{5.2}=2$

Therefore, the correct option is C.